Generalized Ellis-Bronikov traversable wormholes in $f(R)$ gravity with anisotropic dark matter

Abstract

This paper studies generalized Ellis-Bronikov (E-B) traversable wormholes in $f(R)$ extended gravity. We assume that these wormholes are supported by anisotropic dark matter (DM) according to the most often used phenomenological models, namely those of Navarro-Frenk-White (NFW), Thomas-Fermi (T-F), and Pseudo-isothermal (PI). Initially, we obtain the field equations in a general scenario of $f(R)$ theories in the metric formalism for the static and spherically symmetric Morris-Thorne spacetime. Then we particularize to a $f(R)$ model with power-law, including the Starobinky modified gravity. Following, we analyze the energy conditions which are not dependent on the DM models (Null and Weak Energy Conditions -- NEC and WEC) and those which are model-dependent (Strong and Dominant Energy Conditions SEC and DEC). Finally, we compare some E-B wormhole solutions and the mentioned DM models, discussing the feasibility of the wormhole-dark matter system in different scenarios.